YES Input TRS: 1: minus(0(),Y) -> 0() 2: minus(s(X),s(Y)) -> minus(X,Y) 3: geq(X,0()) -> true() 4: geq(0(),s(Y)) -> false() 5: geq(s(X),s(Y)) -> geq(X,Y) 6: div(0(),s(Y)) -> 0() 7: div(s(X),s(Y)) -> if(geq(X,Y),s(div(minus(X,Y),s(Y))),0()) 8: if(true(),X,Y) -> X 9: if(false(),X,Y) -> Y Number of strict rules: 9 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #minus(s(X),s(Y)) -> #minus(X,Y) #2: #div(s(X),s(Y)) -> #if(geq(X,Y),s(div(minus(X,Y),s(Y))),0()) #3: #div(s(X),s(Y)) -> #geq(X,Y) #4: #div(s(X),s(Y)) -> #div(minus(X,Y),s(Y)) #5: #div(s(X),s(Y)) -> #minus(X,Y) #6: #geq(s(X),s(Y)) -> #geq(X,Y) Number of SCCs: 2, DPs: 2 SCC { #6 } POLO(Sum)... succeeded. #div w: 0 s w: x1 + 1 minus w: 0 #geq w: x2 false w: 0 div w: 0 geq w: 0 true w: 0 0 w: 0 if w: 0 #minus w: 0 #if w: 0 USABLE RULES: { } Removed DPs: #6 Number of SCCs: 1, DPs: 1 SCC { #1 } POLO(Sum)... succeeded. #div w: 0 s w: x1 + 1 minus w: 0 #geq w: 0 false w: 0 div w: 0 geq w: 0 true w: 0 0 w: 0 if w: 0 #minus w: x1 + x2 #if w: 0 USABLE RULES: { } Removed DPs: #1 Number of SCCs: 0, DPs: 0